Nonlinear Correlation Spectroscopy (NLCS) Matthias Geissbuehler,* ,†,∥ Luigi Bonacina, ‡ Vladislav Shcheslavskiy, †,§ Noelia L. Bocchio, † Stefan Geissbuehler, † Marcel Leutenegger, † Iwan Ma ̈ rki, † Jean-Pierre Wolf, ‡ and Theo Lasser † † Laboratoire d’Optique Biome ́ dicale LOB, E ́ cole Polytechnique Fé de ́ rale de Lausanne (EPFL), Switzerland ‡ GAP-Biophotonics, Universite ́ de Gene ̀ ve, Switzerland § Becker&Hickl GmbH, Berlin, Germany * S Supporting Information ABSTRACT: We present a novel concept for optical spectroscopy called nonlinear correlation spectroscopy (NLCS). NLCS analyses coherent field fluctuations of the second and third harmonic light generated by diffusing nanoparticles. Particles based on noncentrosymmetric non- linear materials such as KNbO 3 show a strong second as well as third harmonic response. The method and the theory are introduced and experimental NLCS results in fetal calf serum are presented showing the promising selectivity of this technique for measurement in complex biological environ- ments. KEYWORDS: Optical spectroscopy, fluorescence correlation spectroscopy (FCS), nonlinear correlation spectroscopy (NLCS), third-harmonic generation (THG), second-harmonic generation (SHG), nonlinear optics M any important questions in life science and medicine require a sensitivity at the single molecule level. This can be readily offered by fluorescence correlation spectroscopy (FCS). 1−3 FCS is a very popular and versatile tool that can be used to study a multitude of problems such as kinetics of enzymes, 4 RNA hybridization, 5 DNA conformational changes, 6,7 chemical reaction kinetics, 8 studies of phases and other membrane properties (in cellular and model mem- branes), 9−12 diffusion regimes in microchannels, 13 photo- physics of fluorophores, 14 and many more. 8 Current single-molecule methods are limited by their signal- to-noise ratio (SNR) at both short and long observation times. For fast processes, their SNR is determined by the lifetime and quantum yield of fluorescent labels and by the detection efficiency of the instrument. On the other hand, it is also difficult to measure slow processes with fluorescence methods because fluorophores hardly withstand long exposure times but tend to photobleach. Photobleaching typically restricts the total observation time to a few seconds, which complicates characterizing slow processes. In order to overcome these shortcomings, novel techniques based on nonlinear optics such as Raman correlation spectroscopy (RCS), 15 coherent anti- Stokes Raman scattering correlation spectroscopy (CARS- CS), 16,17 correlation spectroscopy of third-harmonic gener- ation, 18 and sum-frequency scattering 19 have been developed. A novel approach named nonlinear correlation spectroscopy (NLCS) is presented here, which is also free from photo- bleaching and has the potential to become a valuable tool for spectroscopic measurements. In classical optics, the induced polarization density depends linearly on the applied electric field P(t)= P lin = ε 0 χ (1) E(t) where χ (1) is the linear susceptibility and ε 0 is the free space permittivity. This holds for weak fields. For high intensities however, the relation becomes nonlinear leading to the generation of higher harmonic light. 20 Techniques based on harmonic generation of light benefit from a coherent signal generation, which allows obtaining relatively strong and stable signals. The strengths of the harmonics scale with the nonlinear susceptibility and the qth power of the incident pumping field, which demands using short pulses of high intensity for good conversion efficiency. Because of the coherent interaction, the phases of all contributing fields should be matched over the lengths of the nonlinear material. In bulk material, the third harmonic (TH) signal vanishes due to the destructive interference of the third harmonic signal generated in front of and behind of the focal plane. This cancelation is due to the Guoy phase shift across the focus. 20,21 On the other hand, nanoparticles (NP) with dimensions comparable to or smaller than the focal volume can generate strong higher harmonic signals. The phase mismatch between the harmonic signals and the incident wave is neglectable (≪π) because NPs are small. Therefore any wavelength can be up- converted. 22 We use a chromium-activated forsterite laser (Cr:forsterite) emitting fs-pulsed light at a central wavelength Received: January 6, 2012 Revised: February 22, 2012 Published: February 29, 2012 Letter pubs.acs.org/NanoLett © 2012 American Chemical Society 1668 dx.doi.org/10.1021/nl300070n | Nano Lett. 2012, 12, 1668−1672